Subset selection for matrices with fixed blocks

doi:10.1007/s11856-021-2171-8

CSpace

	Subset selection for matrices with fixed blocks
	Xie, Jiaxin 1; Xu, Zhiqiang 2,3
	2021-07-02
发表期刊	ISRAEL JOURNAL OF MATHEMATICS
ISSN	0021-2172
页码	26
摘要	Subset selection for matrices is the task of extracting a column sub-matrix from a given matrix B is an element of DOUBLE-STRUCK CAPITAL R-nxm with m > n such that the pseudoinverse of the sampled matrix has as small Frobenius or spectral norm as possible. In this paper, we consider a more general problem of subset selection for matrices that allows a block to be fixed at the beginning. Under this setting, we provide a deterministic method for selecting a column submatrix from B. We also present a bound for both the Frobenius and spectral norms of the pseudoinverse of the sampled matrix, showing that the bound is asymptotically optimal. The main technology for proving this result is the interlacing families of polynomials developed by Marcus, Spielman and Srivastava. This idea also results in a deterministic greedy selection algorithm that produces the sub-matrix promised by our result.
DOI	10.1007/s11856-021-2171-8
收录类别	SCI
语种	英语
资助项目	Beijing Natural Science Foundation[Z180002] ; NSFC[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000669309600009
出版者	HEBREW UNIV MAGNES PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58873
专题	中国科学院数学与系统科学研究院
通讯作者	Xie, Jiaxin
作者单位	1.Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China 2.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Inst Compuat Math, Acad Math & Syst Sci, Beijing 100091, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Xie, Jiaxin,Xu, Zhiqiang. Subset selection for matrices with fixed blocks[J]. ISRAEL JOURNAL OF MATHEMATICS,2021:26.
APA	Xie, Jiaxin,&Xu, Zhiqiang.(2021).Subset selection for matrices with fixed blocks.ISRAEL JOURNAL OF MATHEMATICS,26.
MLA	Xie, Jiaxin,et al."Subset selection for matrices with fixed blocks".ISRAEL JOURNAL OF MATHEMATICS (2021):26.